Senior US diplomats have told leaders in Belgrade that failure to hand over top war crimes suspects will further deepen Serbia-Montenegro's isolation.
Mladic was the Bosnian Serbs' main military commander
The UN tribunal in The Hague is demanding, in particular, the transfer of Ratko Mladic and Radovan Karadzic for crimes during Bosnia's civil war.
President Boris Tadic promised to supply "clear answers" within days.
Belgrade has previously said it does not know the whereabouts of Mr Mladic and Mr Karadzic.
Marc Grossman, a US undersecretary of state, and Richard Prosper, the US roving ambassador for war crimes, met both the Serbia-Montenegrin president and Foreign Minister Vuk Draskovic.
Mr Tadic said he took the Americans' message "extremely seriously".
"This situation warrants clear answers from our side,
from Belgrade, and those answers will come in the next few days," he said.
The Hague has asked Belgrade to extradite more than a dozen war crimes suspects, including four Serbian generals indicted in connection with the conflict in Kosovo.
Mr Grossman stressed that the failure to hand over figures such as Gen Mladic or Mr Karadzic continued to damage the country's prospects.
"I believe Serbia and Montenegro already has [suffered] consequences from the fact that Mladic and the generals are not in The Hague," he said.
"You are held back from European Union integration and Nato's Partnership for Peace programme.
"You don't want Serbia-Montenegro to be an isolated island, and that is happening now."
The US itself is withholding about $30m in aid from Serbia-Montenegro because of the lack of action over the indicted pair.
Mr Grossman welcomed the news that Belgrade prosecutors had issued warrants on Wednesday for the four generals, who may be tried in Serbia-Montenegro under an agreement with the Hague tribunal.
The four - former police chiefs Sreten Lukic and Vlastimir Djordjevic, and retired army generals Nebojsa Pavkovic and Vladimir Lazarevic - were indicted in The Hague last October and the indictments were conveyed to Serbia in July.
Three of the generals are believed to be living openly in Serbia, while the fourth disappeared in 2001 and is thought by some to be in Russia.
The BBC's Matt Prodger reports from Belgrade that international prosecutors doubt Belgrade has the will to put the four on trial.